Reaction rates of

Reactions like the cleavage of chlorine into atoms fall into a special category  

If there is no hill to climb in going from chlorine atoms to a chlorine molecule, but simply a slope to descend, the cleavage of a chlorine molecule must involve simply the ascent of a slope as shown in Fig. 2.4. The Eact for the cleavage of a chlorine molecule, then, must equal the A//, that is, 58 kcal. This equality of and A// is believed to hold generally for reactions in which molecules dissociate into radicals. 

A chemical reaction i the result of collisions of sufficient energy and proper orientation. The rate of reaction, therefore, must be the rate at which these effective collisions occur, the number of effective collisions, let us say, that occur during each second within each cc of reaction space. We can then express the rate as the product of three factors. (The number expressing the probability th at a 

The collision frequency depends upon (a) how closely the particles are crowded together, that is, concentration or pressure (b) how large they are and (c) how fast they are moving, which in turn depends upon their weight and the temperature. 

We can change the concentration and temperature, and thus change the rate. We are familiar with the fact that an increase in concentration causes an increase in rate it does so, of course, by increasing the collision frequency. A rise in temperature increases the collision frequency as we shall see, it also increases the energy factor, and this latter effect is so great that the effect of temperature on collision frequency is by comparison unimportant. 

The reaction scheme obtained after a kinetic analysis can be expressed in the following general form  

Consider a reaction volume where all the state variables (temperature and concentrations for example) have identical values. The molar flow rate of production of the constituent Cj due to this element of volume is therefore well defined. 

The rate of production of Cj will be called Rj, and it is equal to the ratio of the molar flow rate of Cj to the volume being considered. The rate Rj is therefore equal to the quantity of Cj produced per unit volume and per imit time. In SI units, Rj is expressed in mol m 3 s . The rate of production Rj is the difference between two terms  

The terms R- and Rj correspond to a rate of formation and a rate of consumption of Cj, respectively. As a result, Rj is a net rate which can be positive, negative or equal to zero. 

The rates Rj are state functions, that is to say functions of the state variables Cj and T, because, as has already been seen, the values of these properties define the state of a uniform gaseous volume perfectly. 

The rate of reaction is often experimentally determined by relating the reactant (or product) concentration with time. 

For a chemical reaction to be feasible, it must occur at a reasonable rate. Consequently, it is important to be able to control the rate of reaction. Most often, this means making it occur more rapidly. When you carry out a reaction in the general chemistry laboratory, you want it to take place quickly. A research chemist trying to synthesize a new drug has the same objective. Sometimes, though, it is desirable to reduce the rate of reaction. The aging process, a complex series of biological oxidations, believed to involve free radicals with unpaired electrons such as 

This chapter sets forth the principles of chemical kinetics, the study of reaction rates. The main emphasis is on those factors that influence rate. These include 

The rate of a reaction depends on many factors such as the concentration of reactants, the temperature at the time of the reaction, the states of reactants, and catalysts. The rate of a reaction is defined as the change of reactant or product concentration in unit time. If we were to define the rate of a reaction in terms of the reactants, we should define the rate as the rate of disappearance of reactants. If we were to define the rate in terms of the products formed, we should define it as the rate of appearance of products. 

For further exploration of this concept, let s look at a hypothetical reaction. In the hypothetical representative reaction shown below, the small letters denote the coefficients of the corresponding capital letter reactants or products. In this reaction, A and B are reactants, and a and b their coefficients respectively. X and Y are the products, and x and y their coefficients respectively. 

For this reaction, we can represent the rate in terms of the disappearance of each reactant or appearance of each product. The numerators are the concentrations of either the reactant or the product, and At represents the elapsed time. 

We can also represent it in terms of reactant B. That looks the same as the rate in terms of concentration of A. In order to express it in terms of B s concentration, substitute the numerator with the concentration of B. The minus sign convention indicates that the rate is expressed in terms of the rate of disappearance (decreasing concentration) of the reactants. 

Also shown below are the representations of the rate in terms of the products  

The rate of the reaction can be described using the rate-temperature relationship, which is known as the Arrhenius equation 6.13, 

Primary explosives have low values for the activation energy and collision factor compared with secondary explosives. Therefore, it takes less energy to initiate primary explosives and makes them more sensitive to an external stimulus, i.e. impact, friction, etc., whereas secondary explosives have higher values for the activation energy and collision factor, and are therefore more difficult to initiate and less sensitive to external stimulus. 

All explosives undergo thermal decomposition at temperatures far below those at which explosions take place. These reactions are important in determining the stability and shelf life of the explosive. The reactions also provide useful information on the susceptibility of explosives to heat. The kinetic data are normally 

Explosive substance Activation energy E/kJ mol Collision factor A 

Equation 6.14 shows the relationship between the rate of decomposition and temperature, where V is the volume of gas evolved, T is the temperature in °C, k is the reaction rate constant, and C is a constant for the particular explosive. 

To define the rate of a reaction, one of the components must be selected and the rate defined in terms of that component. The rate of reaction is the number of moles formed with respect to time, per unit volume of reaction mixture  

If the rate-controlling step in the reaction is the collision rs = ksCbBCcc. .. .-k sasaT. (5.35) 

The exponent for the concentration (b, c.) is known as the order of reaction. The reaction rate constant is a function of temperature, as will be discussed in the next chapter. Thus, from Equations 5.22 to 5.26  

Reactions for which the rate equations follow the stoichiometry as given in Equations 5.23 to 5.26 are known as elementary reactions. If there is no direct correspondence between the reaction stoichiometry and the reaction rate, these are known as nonelementary reactions and are often of the form  

If the forward and reverse reactions are nonelementary, perhaps involving the formation of chemical intermediates in multiple steps, then the form of the reaction rate equations can be more complex than Equations 5.33 to 5.36. 

An unambiguous rate of reaction, r, is defined by the number of occurrences of this stoichiometric event, such as that shown by reaction 2.2, per unit time. For a particular species, i, its rate of production, ri, is related to r by the stoichiometric coefficient, i.e., 

Rates of reaction can be expressed in terms of process variables associated with a given reactor type via relationships generated by material balances on that reactor. Because rate measurements are essentially always made in a reactor, a discussion of the rate of reaction can be initiated by considering a well-mixed, closed reactor system typically referred to as a batch reactor. In this system, the advancement of the reaction is measured by the molar extent of reaction, and the reaction rate is equivalent to the rate of change of the molar extent of reaction, i.e.. 

Source. H, S. Horned and B. B. Owen, The Physical Chemistry of Bfecfroiyfe Solutions, 3rd ed.. Reinhold, New York, 1958. 

By comparison the free energy change for dissociation of the bisulfide ion, 

Acid-base reactions in aqueous solutions generally proceed extremely rapidly. The reaction. 

At equilibrium, forward rate = reverse rate therefore, 

Substituting for and Jcg and using 55.5 moles/iiter as the concentration of water, we obtain the concentration product of water. 

Not every collision, not every punctilious trajectory by which billiard-ball complexes arrive at their calculable meeting places leads to reaction. 

Men (and women) are not as different from molecules as they think. 

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We notice that while the degree of dissociation, or degree of ionization may have any value from 0- l, the extent of reaction may have (in these two examples) values 0—and respectively. It may 

It is the ratio of the change (positive, zero or negative) in the extent of reaction to the time interval dt (always taken as positive) during which this change takes place. This definition is due to De Donder. 

The rate of reaction can also be expressed in terms of the rate of consumption or production of moles of the components for by (1.42) 

In practice we frequently measure the rate of change of the molar concentration of the components. Since by definition, cf. (1.6), 

Theorem 8.2 - During a mode with one determining step, the rate of the reaction is the product of the reactivity of the determining step (the other steps are at equilibrium) by the space function relative to the zone where the determining step takes place this product is weighted by the inverse of the multiplying coefficient of 

To calculate the rate of our reaction, since the mode is in pseudo-steady state, relation [7.13] should be applied by choosing the step that determines the speed to be step i. Therefore we will have  

In this expression, ( ). is the reactivity of the determining step. All others are 

This form is thus the product of a reactivity )rn = which only depends 

The product of [8.20] enables us to say that, for a linear sequence that occurs in pure mode determined by one step, the rate is separable. 

The terms rate, speed, and velocity are all synonymous in chemical kinetics, though this is not so in mechanics. It takes different periods of time to complete different reactions. The neutralization reaction between acids and bases, mentioned earlier as an example of homogeneous reactions, takes place almost instantaneously at room temperature and under atmospheric pressure. However, it takes many days for iron to rust under these conditions. Thus, the rates of reactions that may take place under the same conditions of temperature and pressure may differ very significantly. When carbon or sulfur or phosphorus bums in 

The form of this functional relationship remains the same, no matter how the rate of the reaction is defined. It is only the constants of proportionality and their dimensions that change while switching over from one definition to another. 

In all chemical reactions it is necessary to know the spontaneity of the reaction thereby indieating the willingness of the reaction to proceed all by itself That a reaction is spontaneous does not neeessarily mean that the reaction also is fast. This means that even if a reaction is spontaneous it may e.g. take many years before the amount of product is sufficient. Hence, it is essential to know something about the rate of reaction. The part of the chemistry is known as chemical reaction kinetic , and this is the subject for the following chapter. 

The production of ammonia NH3 is one of the most important chemical reactions and is used as e.g. fertiliser. Roughly 20 millions tonnes of ammonia is produeed each year. The formation of ammonia may Ifom a thermodynamically viewpoint be expressed as  

Does one however have N2 and H2 on gas form side by side at 25 C, no reaction will take place. This is caused by the faet that the rate of reaction is extremely slow at 25 C. One has to find other methods for produeing NH3 in praetise. This illustrated that even if the reaetion aetually may proceed from a thermodynamie point of view and even if the stoichiometry fits it is not certain that the reaction actually will take plaee fast enough to exploit the reaetion in praetise. It is necessaiy in addition to know something about the rate of reaetion. 

We will introduce the term reaction velocity in this chapter. For a chemical reaction it is the concentration of reactants or products changing with time. For an arbitrary specie A with the concentration in moles/litres the rate of reaction may be expressed as  

In an experiment we begin by having a flask of gas filled with NO2 at room temperature (25 C). At this temperature NO2 is stabile, but if the gas is heated up to 300 C, it decompose to NO and O2 following the following reaction scheme  

The values for the activation energy can be used to measure the ease with which an explosive composition will initiate, where the larger the activation energy the more difficult it will be to initiate the explosive composition. 

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The choice of reactor temperature depends on many factors. Generally, the higher the rate of reaction, the smaller the reactor volume. Practical upper limits are set by safety considerations, materials-of-construction limitations, or maximum operating temperature for the catalyst. Whether the reaction system involves single or multiple reactions, and whether the reactions are reversible, also affects the choice of reactor temperature, as we shall now discuss. 

Increasing the pressure of irreversible vapor-phase reactions increases the rate of reaction and hence decreases reactor volume both by decreasing the residence time required for a given reactor conversion and increasing the vapor density. In general, pressure has little effect on the rate of liquid-phase reactions. 

Most processes are catalyzed where catalysts for the reaction are known. The choice of catalyst is crucially important. Catalysts increase the rate of reaction but are unchanged in quantity and chemical composition at the end of the reaction. If the catalyst is used to accelerate a reversible reaction, it does not by itself alter the position of the equilibrium. When systems of multiple reactions are involved, the catalyst may have different effects on the rates of the different reactions. This allows catalysts to be developed which increase the rate of the desired reactions relative to the undesired reactions. Hence the choice of catalyst can have a major influence on selectivity. 

Catalytic gas-phase reactions play an important role in many bulk chemical processes, such as in the production of methanol, ammonia, sulfuric acid, and nitric acid. In most processes, the effective area of the catalyst is critically important. Since these reactions take place at surfaces through processes of adsorption and desorption, any alteration of surface area naturally causes a change in the rate of reaction. Industrial catalysts are usually supported on porous materials, since this results in a much larger active area per unit of reactor volume. 

An excess of ammonia in the reactor decreases the concentrations of monoetha-nolamine, diethanolamine, and ethylene oxide and decreases the rates of reaction for both secondary reactions. 

Generally speaking, temperature control in fixed beds is difficult because heat loads vary through the bed. Also, in exothermic reactors, the temperature in the catalyst can become locally excessive. Such hot spots can cause the onset of undesired reactions or catalyst degradation. In tubular devices such as shown in Fig. 2.6a and b, the smaller the diameter of tube, the better is the temperature control. Temperature-control problems also can be overcome by using a mixture of catalyst and inert solid to effectively dilute the catalyst. Varying this mixture allows the rate of reaction in different parts of the bed to be controlled more easily. 

Although the catalyst affects the rate of reaction, it cannot affect the position of equilibrium in a reversible reaction. 

Michaelis constant An experimentally determined parameter inversely indicative of the affinity of an enzyme for its substrate. For a constant enzyme concentration, the Michaelis constant is that substrate concentration at which the rate of reaction is half its maximum rate. In general, the Michaelis constant is equivalent to the dissociation constant of the enzyme-substrate complex. 

While there is some question about the interpretation of absolute AV values, such measurements are very useful as an alternative means of determining the concentration of molecules in a film (as in following rates of reaction or... 

The usual situation, true for the first three cases, is that in which the reactant and product solids are mutually insoluble. Langmuir [146] pointed out that such reactions undoubtedly occur at the linear interface between the two solid phases. The rate of reaction will thus be small when either solid phase is practically absent. Moreover, since both forward and reverse rates will depend on the amount of this common solid-solid interface, its extent cancels out at equilibrium, in harmony with the thermodynamic conclusion that for the reactions such as Eqs. VII-24 to VII-27 the equilibrium constant is given simply by the gas pressure and does not involve the amounts of the two solid phases. 

Figure A3.12.10. Schematic diagram of the one-dimensional reaction coordinate and the energy levels perpendicular to it in the region of the transition state. As the molecule s energy is increased, the number of states perpendicular to the reaction coordinate increases, thereby increasing the rate of reaction. (Adapted from [4].)...

Efficient use of a catalyst requires high rates of reaction per unit volume and, since reaction takes place on the surface of a solid, catalysts have high surface areas per unit volume. Therefore, tlie typical catalyst is porous, witli... 

Figure C2.7.10. Rates of reaction of CO with O on Pt(l 11), detennined from microscopic ( ) and macroscopic (+) ( text for details 1121.

If a compact film growing at a parabolic rate breaks down in some way, which results in a non-protective oxide layer, then the rate of reaction dramatically increases to one which is linear. This combination of parabolic and linear oxidation can be tenned paralinear oxidation. If a non-protective, e.g. porous oxide, is fonned from the start of oxidation, then the rate of oxidation will again be linear, as rapid transport of oxygen tlirough the porous oxide layer to the metal surface occurs. Figure C2.8.7 shows the various growth laws. Parabolic behaviour is desirable whereas linear or breakaway oxidation is often catastrophic for high-temperature materials. 

Obtain five small dry test-tubes (75 x 10 mm. ) and introduce 1 ml. of the following alcohols into each ethyl alcohol, n-butyl alcohol, jcc.-butyl alcohol, cycZohexanol and butyl alcohol. Add a minute fragment of sodium to each and observe the rate of reaction. Arrange the alcohols in the order of decreasing reactivity towards sodium. 

It is obvious that the reaction is accelerated markedly by water. However, for the first time, the Diels-Alder reaction is not fastest in water, but in 2,2,2-trifiuoroethanol (TFE). This might well be a result of the high Bronsted acidity of this solvent. Indirect evidence comes from the pH-dependence of the rate of reaction in water (Figure 2.1). Protonation of the pyridyl nitrogen obviously accelerates the reaction. 

Nitric acid being the solvent, terms involving its concentration cannot enter the rate equation. This form of the rate equation is consistent with reaction via molecular nitric acid, or any species whose concentration throughout the reaction bears a constant ratio to the stoichiometric concentration of nitric acid. In the latter case the nitrating agent may account for any fraction of the total concentration of acid, provided that it is formed quickly relative to the speed of nitration. More detailed information about the mechanism was obtained from the effects of certain added species on the rate of reaction. 

The phenomenon was established firmly by determining the rates of reaction in 68-3 % sulphuric acid and 61-05 % perchloric acid of a series of compounds which, from their behaviour in other reactions, and from predictions made using the additivity principle ( 9.2), might be expected to be very reactive in nitration. The second-order rate coefficients for nitration of these compounds, their rates relative to that of benzene and, where possible, an estimate of their expected relative rates are listed in table 2.6. 

The possibility that the rate of reaction of benzene is affected by the phenomenon of reaction at the encounter rate is a matter of importance, because benzene is the datum relative to which comparisons of reactivity are made. Up to 68 % sulphuric acid the slope of a plot of log [kffi moU s i) against — + log is unity for data relating to 25 °C, and... 

The results in table 2.6 show that the rates of reaction of compounds such as phenol and i-napthol are equal to the encounter rate. This observation is noteworthy because it shows that despite their potentially very high reactivity these compounds do not draw into reaction other electrophiles, and the nitronium ion remains solely effective. These particular instances illustrate an important general principle if by increasing the reactivity of the aromatic reactant in a substitution reaction, a plateau in rate constant for the reaction is achieved which can be identified as the rate constant for encounter of the reacting species, and if further structural modifications of the aromatic in the direction of further increasing its potential reactivity ultimately raise the rate constant above this plateau, then the incursion of a new electrophile must be admitted. 

The observation of nitration in nitromethane fully dependent on the first power of the concentration of aromatic was made later. The rate of reaction of /)-dichlorobenzene ([aromatic] = 0-2 mol [HNO3] = 8-5 mol 1 ) obeyed such a law. The fact that in a similar solution 1,2,4-trichlorobenzene underwent reaction according to the same kinetic law, but about ten times slower, shows that under first-order conditions the rate of reaction depends on the reactivity of the compound. 

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